equation 14.86 eq:lie-sopq-gen

open in the book · parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2379

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depends_on definition 14.63 Pauli–Lubanski vector ¶
- depends_on lemma 14.64 Properties of $W$ ¶
  - depends_on theorem 14.65 The two Casimir operators of the Poincaré algebra in $3+1$ dimensions ¶
    - depends_on example A.394 $D = 4$ ¶
- depends_on theorem 14.65 The two Casimir operators of the Poincaré algebra in $3+1$ dimensions ¶ ↺
depends_on proposition 14.117 The quadratic invariant and its Chern–Simons form ¶
depends_on proposition 14.59 The Killing fields of a flat pseudo-Euclidean space ¶
- depends_on corollary A.344 The algebras $\mathfrak{so}(p,q)$ are semisimple ¶
  - depends_on corollary A.411 Semisimple algebras admit no nontrivial extension ¶
  - depends_on example A.359 The Lorentz algebra ¶
- depends_on proposition 14.69 The de~Sitter algebras are isometry algebras ¶

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type	direction	node	provenance	where
`depends_on`	←	Pauli–Lubanski vector	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2847
`depends_on`	←	The quadratic invariant and its Chern–Simons form	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:5194
`depends_on`	←	The Killing fields of a flat pseudo-Euclidean space	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:2411